arXiv subjects

Kleyton da Costa

Publications and source records attributed to Kleyton da Costa.

7 recordsLinked to original sources

arXiv2026

When Should Graph Attention Be Sparse? Learning a Per-Edge Tsallis Index

Graph attention normalizes neighborhood scores with softmax, the maximum-entropy choice under Shannon statistics. But homophilic and heterophilic graphs want different attention shapes, and one fixed normalization cannot serve both. We propose \textbf{LTGA} (\textbf{L}earnable \textbf{T}sallis \textbf{G}raph \textbf{A}ttention), a graph attention layer whose Tsallis entropic index $q$ is learned jointly with the weights, interpolating continuously between heavy-tailed ($q\!<\!1$), softmax ($q\!=\!1$) and compact-support ($q\!>\!1$) attention at four granularities from a global scalar to a per-edge index, under a bounded reparameterization that starts every model at the GAT baseline. Across eight benchmarks at ten seeds, LTGA-Edge takes the best average rank ($2.75$), but the omnibus test does not reject ($p\!=\!0.199$) and learning $q$ does not beat searching it: a validation-tuned frozen grid reaches $61.4\%$, tuned $α$-entmax $62.2\%$ and a capacity-matched $q\!\equiv\!1$ control $62.0\%$, against $61.7\%$ for LTGA-Edge. What the learned index buys is one run instead of a grid, and an interpretable mechanism: where $q$ leaves $1$, it prunes $42\%$ of attention coefficients to exactly zero, and those edges are selectively the wrong ones, restoring them costs $7.1$ points, while random pruning at the same rate costs $13.0$ more. Project page: https://kleyt0n.github.io/ltga

cs.LG↗

arXiv2026

Perspectives on Tsallis Statistics for Artificial Intelligence

Tsallis statistics generalizes Boltzmann-Gibbs statistical mechanics through a single real parameter $q$ that controls the weight assigned to rare and frequent events. Originally proposed to describe physical systems with long-range correlations, multifractal geometry, and heavy-tailed fluctuations, the framework has become a recurring ingredient in modern artificial intelligence (AI): it underlies sparse attention mechanisms (\textsc{sparsemax} and $α$-\textsc{entmax}), maximum-entropy reinforcement learning with controllable exploration, robust and heavy-tailed probabilistic models, and a family of generalized loss functions and regularizers. This paper offers a structured perspective on where Tsallis statistics meets AI. We first review the mathematical core: $q$-entropy and its variational (maximum-entropy) foundation, the $q$-exponential and $q$-logarithm, the $q$-central limit theorem, $q$-Gaussian distributions, and their dynamical origin in superstatistics, emphasizing the properties that matter for machine learning. We then survey applications across softmax generalization, reinforcement learning, sequential and graph neural models, generative and probabilistic modeling, loss design, and optimization, extracting the recurring design pattern in each case: a tunable interpolation between dense/uniform and sparse/peaked behavior governed by $q$. We further argue that the heavy-tailed weight spectra and gradient-noise statistics empirically observed in deep networks are themselves nonextensive signatures, placing modern learning dynamics within the scope of $q$-statistics. Finally, we discuss methodological pitfalls, the relationship to information geometry and $q$-exponential families, and open directions, arguing that $q$ should be treated as a learnable inductive bias rather than a fixed hyperparameter.

cs.AI↗

arXiv2026

GraphNetz: Statistical Benchmarking of Graph Neural Networks with Paired Tests and Rank Aggregation

Graph Neural Networks (GNNs) benchmarks often report single point estimates, even when performance differences are small relative to variation across random seeds, train/test splits, and datasets. Confidence intervals, paired comparisons, multiple-comparison correction, and rank-based aggregation are standard statistical tools, but they are rarely the default output of graph-learning benchmark suites. We introduce GraphNetz, a benchmarking framework whose default output is a structured statistical report rather than a raw accuracy table. GraphNetz currently includes 63 dataset loaders, four task types, and five canonical GNN architectures, while also supporting custom datasets and models. The framework standardizes multi-seed evaluation and automatically returns per-cell confidence intervals, Holm-corrected paired tests, and Friedman-Nemenyi critical-difference diagrams across tasks. In a cross-category benchmark over ten heterogeneous tasks, apparent rank differences among four canonical node-level encoders fall within a single Nemenyi clique, indicating that none is significantly better than the others at $α= 0.05$. GraphNetz therefore provides researchers with a reproducible computational and statistical pipeline to benchmark new graph-learning methods against standard architectures, over different tasks and a wide set of applications, while reporting principled statistical evidence for benchmarking which accounts for seed uncertainty. This framework is set to serve the graph-learning community with a reproducible and honest model comparison ready to be added to papers.

cs.CE↗

arXiv2026

Divergence-Guided Particle Swarm Optimization

Particle Swarm Optimization (PSO) is susceptible to premature convergence when the swarm collapses around the global best, particularly on multimodal landscapes in higher dimensions. We propose Divergence-guided PSO (DPSO), which augments the velocity update with a modulation term that repels particles whose personal bests have converged near the global best. The repulsion is gated by a Gaussian similarity kernel, which we prove is equivalent to an exponentially decaying function of the KL divergence between Gaussian-embedded personal and global bests, connecting the mechanism to the family of $f$-divergences and providing a principled basis for kernel design. Experiments on 36 benchmark functions (15 unimodal, 21 multimodal) across dimensions $D \in \{10, 30, 50\}$, each with 30 independent runs, show that DPSO frequently outperforms standard PSO on multimodal problems, with improvements of 2-8$\times$ on functions such as Pinter, Ackley, and Levy, and up to 5$\times$ reduction in run-to-run variance. On unimodal landscapes the modulation term is counterproductive, confirming that DPSO targets the exploration-exploitation trade-off rather than offering a universal improvement. The method adds one hyperparameter, incurs 15--25\% wall-clock overhead, and does not increase the asymptotic per-iteration complexity of PSO. The project code is available here: https://github.com/Kleyt0n/dpso

cs.CE↗

arXiv2024

Evaluating Explainability in Machine Learning Predictions through Explainer-Agnostic Metrics

The rapid integration of artificial intelligence (AI) into various industries has introduced new challenges in governance and regulation, particularly regarding the understanding of complex AI systems. A critical demand from decision-makers is the ability to explain the results of machine learning models, which is essential for fostering trust and ensuring ethical AI practices. In this paper, we develop six distinct model-agnostic metrics designed to quantify the extent to which model predictions can be explained. These metrics measure different aspects of model explainability, ranging from local importance, global importance, and surrogate predictions, allowing for a comprehensive evaluation of how models generate their outputs. Furthermore, by computing our metrics, we can rank models in terms of explainability criteria such as importance concentration and consistency, prediction fluctuation, and surrogate fidelity and stability, offering a valuable tool for selecting models based not only on accuracy but also on transparency. We demonstrate the practical utility of these metrics on classification and regression tasks, and integrate these metrics into an existing Python package for public use.

cs.LG↗

arXiv2023

Anomaly Detection in Global Financial Markets with Graph Neural Networks and Nonextensive Entropy

Anomaly detection is a challenging task, particularly in systems with many variables. Anomalies are outliers that statistically differ from the analyzed data and can arise from rare events, malfunctions, or system misuse. This study investigated the ability to detect anomalies in global financial markets through Graph Neural Networks (GNN) considering an uncertainty scenario measured by a nonextensive entropy. The main findings show that the complex structure of highly correlated assets decreases in a crisis, and the number of anomalies is statistically different for nonextensive entropy parameters considering before, during, and after crisis.

cs.AI↗

arXiv2022

A Systematic Comparison of Forecasting for Gross Domestic Product in an Emergent Economy

Gross domestic product (GDP) is an important economic indicator that aggregates useful information to assist economic agents and policymakers in their decision-making process. In this context, GDP forecasting becomes a powerful decision optimization tool in several areas. In order to contribute in this direction, we investigated the efficiency of classical time series models, the state-space models, and the neural network models, applied to Brazilian gross domestic product. The models used were: a Seasonal Autoregressive Integrated Moving Average (SARIMA) and a Holt-Winters method, which are classical time series models; the dynamic linear model, a state-space model; and neural network autoregression and the multilayer perceptron, artificial neural network models. Based on statistical metrics of model comparison, the multilayer perceptron presented the best in-sample and out-sample forecasting performance for the analyzed period, also incorporating the growth rate structure significantly.

econ.EM↗